Results of nonequilibrium molecular dynamics simulations of vibrational energy relaxation of azulene in carbon dioxide and xenon at low and high pressure are presented and analyzed. Simulated relaxation times are in good agreement with experimental data for all systems considered. The contribution of vibration-rotation coupling to vibrational energy relaxation is shown to be negligible. A normal mode analysis of solute-to-solvent energy flux reveals an important role of high-frequency modes in the process of vibrational energy relaxation. Under all thermodynamic conditions considered they take part in solvent-assisted intramolecular energy redistribution and, moreover, at high pressure they considerably contribute to azulene-to-carbon dioxide energy flux. Solvent-assisted (or collision-induced) intermode energy exchange seems to be the main channel, ensuring fast intramolecular energy redistribution. For isolated azulene intramolecular energy redistribution is characterized by time scales from several to hundreds of ps and even longer, depending on initial excitation. The major part of solute vibrational energy is transferred to the solvent via solute out-of-plane vibrational modes. In-plane vibrational modes are of minor importance in this process. However, their contribution grows with solvent density. The distribution of energy fluxes via azulene normal modes strongly depends on thermodynamic conditions. The contribution of hydrogen atoms to the overall solute-to-solvent energy flux is approximately two to three times higher than of carbon atoms depending on the system and thermodynamic conditions as well. Carbon atoms transfer energy only in the direction perpendicular to the molecular plane of azulene, whereas hydrogen atoms show more isotropic behavior, especially at high pressure.